# Teaching

• ### Curricular goals and assessment challenges in statistics education

This chapter frames the main issues with which this volume deals. The chapter examines common goals for statistics education at both precollege (school) and college levels, describes the resulting challenges for assessment in statistics education, and outlines the main issues addressed by each of the chapters in this volume. Finally, needs for future research and development are discussed.

• ### Monitoring attitudes and beliefs in statistics education

Students' attitudes and beliefs can impede (or assist) learning statistics, and may affect the extent to which students will develop useful statistical thinking skills and apply what they have learned outside the classroom. This chapter alerts educators to the importance of assessing student attitudes and beliefs regarding statistics, describes and evaluates different methods developed to assess where students stand in this regard, provides suggestions for using and extending existing assessments, and outlines future research and instructional needs.

• ### A framework for assessing knowledge and learning in statistics (K-8)

This chapter provides an overview for thinking about what teachers and students should know and be able to do with respect to learning statistics at the K-8 levels. Given the number of concepts to be considered and our limited knowledge about the complexities of learning these concepts, we focus on the understanding of graphical representations, examine examples of "good tasks" that may be used to assess graph knowledge, and reflect on what we have learned about the complexities of assessing students' graph knowledge, when using these tasks.

• ### Simple approaches to assessing underlying understanding of statistical concepts

Statistics should be introduced with clear linkages to the mathematics that students already understand and within contexts that students find meaningful. Otherwise, students may learn statistics in rote fashion or apply statistics in a merely instrumental fashion and draw erroneous conclusions from data. In this chapter we present two examples of the use of simple assessment techniques that uncovered students' poor understanding of statistical concepts.

• ### Assessing statistical thinking using the media

The goals of this chapter are (a) to address the need to assess statistical thinking as it occurs in social settings outside the classroom, (b) to suggest a hierarchy for judging outcomes, (c) to provide examples of viable assessment based on items from the media, and (d) to discuss the implications for classroom practice.

• ### Assessing student projects

The main purpose of this chapter is to offer practical advice to teachers who want to use projects in their courses. In this chapter some examples of projects are given, two assessment models are explained, and teachers' experiences are described. The project models and examples described have been used with students of 14 to 18 years of age, but can be adapted for younger or older students as well.

• ### Assessing project work by external examiners

Over a number of years the external examiners of a regional statistics course for 18-year-old students in schools and colleges in the United Kingdom became aware that the method of assessment was distorting the teaching and learning process, that the things being assessed were not the things that the examiners thought most important for the students to know. This chapter shows how the assessment methods were changed by adding in a compulsory project and reflects on the impact of this change on the teaching and learning of statistics.

• ### Portfolio assessment in graduate level statistics courses

In this chapter, the process of developing a form of alternative assessment, the portfolio, will be described. The portfolio is a purposeful collection of student work that exhibits the student's efforts, progress and achievements over time. Portfolio develpment supports the assessment of long-term projects, encourages student-initiated revision and provides a context for presentation, guidance, and critique. The purpose of portfolio development is the same no matter the course or age of the students, to display the products of instruction in a way which challenges teachers and students to focus on meaningful outcomes. The context in which the use of portfolios is described here is a graduate level statistics course where an additional purpose is to provide students with an organized reference on statistical programming, analylsis, and interpretation. However, the process used in developing portfolios and the important issues surrounding portfolio assessment can easily be generalized to different educational levels and subject areas. Some of the questions addressed in this chapter are 1) What is the underlying belief concerning knowledge construction which guides portfolio assessment?, 2) How do you develop and use portfolios?, 3) What does a portfolio look like?, and 4) What are the major considerations in deciding to use portfolio assessment?

• ### Issues in constructing assessment instruments for the classroom

When constructing assessment instruments both the purpose of the assessment (feedback, grading) and the skills which are being assessed need to be considered. The main purpose of this chapter is to help teachers develop their own assessment instruments by giving specific examples of tasks. Unsatisfactory tasks are used to illustrate the pitfalls, and alternative versions are given as examples of good practice. Some comments on grading are included. The emphasis is on written assessment in the classroom, mainly of pupils aged about 14-19, but much is relevant also to introductory statistics courses at college and university level. Consideration is given to ways of assessing factual knowledge, the ability to use computers, understanding of concepts and application of techniques, and communication skills. The pros and cons of multiple choice and open-ended questions are discussed as are the challenges of oral assessment and assessment of group work.

• ### Assessment on a budget: Using traditional methods imaginatively

Because many of the authentic assessment methods described in this book tend to be very demanding of teacher-time, there is still an important place for finding ways to employ inexpensive, traditoinal methods more creatively in an attempt to come closer to achieveing the same goals that those who advocate authentic assessment methods are targeting. The basic idea is to identify the elements of statistical thinking that we want to foster and then find ways of testing these elements with objective assessment methods (in particular, multiple choice). The chapter explores the extent to which objective testing can approximate the results of authentic assessment techniques and the extent to which it falls short. We provide guidelines for the writing of objective test items, together with examples.